Tangent planes
Disclaimer: Our central goal in making this page was to explore the use of some of the new technology at our disposal. Using dreamweaver, transforming Maple documents to webpages, (including gifs), and learning how to provide worksheets for dowload were some of the technology goals we had set for ourselves.
You already know from previous calculus courses that the tangent line is the best "linear approximation" to the graph of a function at any given point, as illustrated below:
In a similar way, the tangent plane to
a surface at a point is the best "linear approximation" to the surface. In
the following you can see the tangent plane at the point (1,-1,6) on the surface
that is the graph of 
. Press "Start" to see the tangent plane from different
viewpoints.
In what sense could we regard the tangent plane as the best linear approximation? Look closely as we zoom in
Click on the button below. This will download a worksheet file that you can open in your CAS, and use to explore tangent lines and tangent planes more fully. In particular this worksheet includes a "maplet" for drawing tangent lines to a curve of your choice.
|